- After reading the preface and Chapter 1, what logic do you find for joining Understanding by Design and Differentiation? In what ways do these arguments make sense for your school?
- The axioms in this chapter reveal beliefs that guided development of Understanding by Design. The corollaries following each axiom reveal beliefs that guided development of Differentiated Instruction.
- Look at each set of axioms and corollaries and discuss what would happen if educators focused their practice on the axioms without the associated corollaries or on the corollaries without the preceding axiom? Do you see either omission happening in classroom practice in your school or district? Do you see practice which sometimes disregards elements of both axioms and corollaries in a set? What are likely outcomes of the omissions? How would the scenarios differ if the teachers in them disregarded the axioms, corollaries, or both?
- What other axioms or corollaries would you propose for the list offered in Chapter 1?

## Thursday, June 4, 2009

### Chapter 1: UbD and DI: An Essential Partnership

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## 9 comments:

1. The marriage between Differentiated Instruction and Understanding by Design is both a logical and useful framework for teaching. In order to facilitate “effective” and “meaningful” learning, one cannot emphasize curriculum at the expense of instruction or vice versa. The framework is useful for our school because it skillfully promotes a common objective and unifying vision for our staff.

2. A & B. Unfortunately some educators do focus their practice on the axioms without the associated corollaries and vice versa.While even more disturbing, some educators in this district are more concerned with the cultivation of self-esteem than the promotion of learning, especially in the arena of alternative education. Oftentimes the omission or disregard for the axioms and corollaries results in a student wondering aloud, “how does this apply to my life?” It is incumbent upon educators to make the learning process “relevant” to students who can then apply their knowledge to real life situations. I think the axioms and corollaries discussed in chapter 1 are sufficient and need no further extrapolation.

1. It makes sense to combine Understanding by Design and Differentiating Instruction because either one without the other weakens the educational experience for most students. A class rich with creative approaches to "reaching" various types of learners but that does not provide challenging new knowledge/skills, or vice-versa, just isn't effective enough. Powell is a high-functioning school with a staff who takes pride in teaching well. This notion is not unusual or impossible.

2. a. If a teacher adhered only to the corollaries without the axioms, or followed the axioms without regard to the corollaries, the result could be instruction that is too vast/broad or too spastic/insignificant. I can only speak for my own classroom when I admit that constant, conscious combining of axioms and corollaries in every lesson/assignment may need improvement. It could be presumed that somewhere in our school and district some teachers run their classrooms or at least particular units without the guidance of axioms/corollaries. This happens because teachers keep using "pet" projects that are hard to let go but that do not benefit students enough anymore. In the scenarios if Mr. Axelt had not allowed axioms and corollaries to guide his lessons and classroom management, he would not have empowered his students to become learners. He would have represented the "sage on the stage" instead of the "guide on the side." By sticking with a traditional role, his diverse students would have received a generic experience day after day, and most would not have grown academically and socially.

2. b. So far I cannot think of any other axioms or corollaries to add to the current seven, though more may occur to me throughout the book. I hope I am seeing creativity, student choice, and parent support woven into the ideas presented in Chapter 1.

1. When planning with intent educators think of who (students), what (curriculum), when (sequence), where (learning environment), how ( delivery and lessons), and why (relevance). These two "ways of thinking" encompass these questions of intentional planning so all students learn, allowing for varying entry and exit levels. Our school's students are everchanging and we will continue to have varying levels of students within each classroom, as well as each unit of study. Teaching to the middle does not address this issue of the variety of student levels of understanding and skill. Best practices included in DI and UbD and intentional planning do address these issues.

2. Focusing practice on axioms without corollaries gives a teacher a general idea, but no concrete thougths as to how to apply it to the students, planning, and/or assessing. Focusing on corollaries, and not including the axioms they fall under, might leave the educator without a true goal in mind.

Many teachers are more comfortable teaching by using specific materials created by a publisher who does not have the same curriculum in mind as our district and/or state standards. The publisher does not, and cannot know, the individual needs of every student (fundamental ideas of the axioms). Therefore the needs of students' understanding and skills drive the planning and implementation (ways in which we address those needs, corollaries), not the scope and sequnce of the materials.

If the teachers in the scenarios provided in chapter 1 disregarded the axioms, corollaries, or both there would be students left unchallenged or confused on either end of the spectrum. The students would also fail to see the value in the content or skills they need to have in order to become productive and contributing members of our society.

2b. If I were to add an axiom and corollary that would benefit the list and all teachers' thoughts, I would include: Students' confidence must be at level which will allow them to take risks when disequilibrium occurs. Without a certain level of confidence, they will not attempt activities or be open to new ways of thinking.

Teachers can build and encourage a students' level of confidence by establishing relationships with all students and creating a sense of community and mutual respect for the differences in his/her classroom.

UbD is focused mostly on curriculum design and student assessment to test the design. Differentiated Instruction looks at ways of meeting individual student needs so they can access the curriculum and have success with the curriculum. It is a logical “marriage” if we want all students to be successful.

The UbD way of thinking is like a road map a teacher designs that is sensitive to not only the ultimate destination, but knows what it looks like upon arrival. So, arriving at Rome, GA would look different than arriving at Rome, Italy. The road map has milestones or important landmarks along the way so that the teacher can check to see if the route is meeting the ultimate goal and is efficient. If the teacher is fortunate she can check her progress with colleagues and develop more efficient and effective means of travel. Oh, and by the way the teacher is in charge of a caravan of students that must all get to the destination. Some are on motorcycles and some are on tricycles, and some are in Maseratis.

So, if we are only concerned with the destination and the process of getting there we could arrive at the destination without our caravan. On the other hand, if we only were concerned with the corollaries the tricycles, motorcycles, and Maseratis would be confused about their direction and speed. If the essential learning is clear, and the path(s) are known then students and teachers can work together toward meaningful achievement.

In Chapter 1, Mr. Axelt asks the reflective question, “What does it mean for my students to understand this topic in ways that are relevant, are authentic, and give them power as learners?” I am also reminded that when Hollywood does a story about teaching and learning, the teacher always has to find a way for the students to apply the learning in a personal way that fits their culture. I have seen teachers at Powell do this, but I am not sure we begin each topic with those questions in mind. I know we are capable of making this happen. I think Axiom 2 (Evidence of student learning is revealed when students apply (transfer) knowledge in authentic contexts) is the most powerful of all the axioms especially when combined with Mr. Axelt’s question. So, I would say that an Axiom I would like is: Student learning must occur in a relevant context that gives students authentic power. On the other hand,I really think Chelsea's axiom/corollary is a pedagogical pre-requisite to mine.

1. I find it very helpful to integrate the two strands of best practice in curriculum and instruction, UbD and DI, to inform teachers as we create learning goals and activities based on state standards, district curriculum and our students' needs. The logic of joining the two models is in the thinking, dialogue, and collaboration teachers use to include the who, what, where, and how that must be considered in lesson design. Correlating the two models helps ensure that all areas of best practice are considered, I saw this starting to happen at Powell in the PLC work, and hope we can continue to develop these skills of collaboration as we plan for student achievement in learning.

2a. If we as teachers focus solely on the axioms, which could become curriculum-centered or teacher-centered, some learners could be left behind or miss essential learning. On the other hand, if the corollaries were applied without much thought to the axioms, learners could be missing essential content for understanding. The two ways of thinking about education complement one another and give teachers more dynamic ways to facilitate student learning.

2b. If I were to add anything to the given axioms and corollaries, I would like to add my support to the ideas in Axiom 2's scenario in which Mr. Axelt worked with the media specialist to provide reading materials and bookmarked websites on a variety of reading levels for the students' better understanding of the concepts of rights and responsibilities in the U.S. Constitution. As students are working on building background knowledge about the U.S. Constitution in order to create their own (authentic) Charter, this is a good time to have available differentiated materials, print and online including the school's subscription databases.

1. Having a destination in mind as well as a path to reach it is very simple logic. Our charge as educators however, is to have different levels of reaching a destination of knowledge and understanding as well as multiple means of traveling there. We must have differentiation of learner objectives as well as means of instruction to help the kids reach the learning goals. Where I struggle with this is the nasty, four letter word of TIME. I just need to get more efficient I suppose.

2. Was I the only one who had to look up the word “corollary”? Who even uses the word “axiom” these days either? Geez, this is a rough start to things. Thankfully this question is easy to answer: by definition, a corollary is only made true by its preceding axiom. I think… :)

So, anyway… none of the axioms would be worthwhile without a specific means of attaining the ideal, nor would the corollaries have been possible without the underlying focused goals that shaped them. Yet, do we as professionals sometimes put the cart before the horse? Overload the cart itself? Forget that our horse is too young to follow the path without guidance? Forget that the horse is far more concerned with the strange look that girl gave him than my physics lesson? Yup. The outcomes are often a significant percentage of the students do not meet the learner objectives. This occurs because the objective itself may not be clear, its relevance to standards may no longer apply, or the means of reaching the objectives with respect to individual needs may not be focused. I freely admit, that on occasion I will show up and teach a lesson from scratch without due preparation and foresight into my individual student’s needs. Life and all its fantastic and sudden splendors will at times dictate our level of preparedness…

I don’t see much else to add the axioms just yet. Of course, I am not quite in my school mindset at the moment. Rather, I am plotting a nice hike with my wife in the morning. :)

1. Phenomenal teachers have been combining solid curriculum (UbD) and meeting individual student needs (DI) for years. So of course I think these two ideas logically go hand in hand. However, for Powell I think it is time for us all to take a fresh look at these ideas. For as Wally alluded to, 'life happens' and we get caught up with a million different things and frequently don't take the time to step back and really ensure that we using all the tools we have to effectively meet students' needs. I think for many of us these are not new ideas but instead an important practice that needs to be reintroduced as we look at the ever changing needs of the students we work with.

2a. Each axiom and its corollaries need to be used together. Curriculum is only effective if it is delivered in ways that students can learn. If the curriculum is fabulous but does not take into account the strategies for helping ALL students become learners then there will be students who do not learn. I think a major challenge for us being middle school teachers is that many students have already experienced this for years. Their needs were not being met but the teachers were being pressured to 'get through the curriculum' so even though some students were not learning the material they were forced to move on leaving these students behind. Now six or seven years later they arrive in our classrooms totally defeated, feeling 'stupid'. So of course to save face they become behavior problems, class clowns, etc. This means that we not only have to have the axioms in place but we also need the resulting corollaries in place in order to help all students become successful members of society.

2b. I, like Wally, am not totally in school mode so it is hard to think of things that may be missing, however, I did love Chelsea's added axiom, “Students' confidence must be at level which will allow them to take risks when disequilibrium occurs.” I whole-heartedly agree with this statement and I feel that building a relationship based on trust and respect is of the utmost importance so students feel safe to take risks in the classroom.

1. Shivamoksha’s comment that Differentiated Instruction and Understanding by Design is a marriage, or in my way of thinking a partnership, is dead on. The logic behind using this methodology for forming classroom practices is deeply rooted in best practices and upheld in many different forms of research. While Powell tends to have students that are high achieving because of internal (and external) drive, we cannot ignore those students who ask the question, “How does this relate to me?” or the students who do not perform to the high level we have come to expect is innate in our student body.

2a. While I believe that I had a strong education, I was struck by how this question made me reflect on the practices used when I was in school. I believe that frequently I had teachers who were either stuck in the axioms alone or focused on an isolated corollary. I liked school and was a rule follower, so I don’t believe my learning was hurt. However, I know that there were many around me who did not get the full benefit they should have because they did not see, and were not shown, the inherent value of the learning we were being asked to do. In many cases, to ask “Why?” was not acceptable, but in many cases this is exactly the question we (both teachers and students) should have been asking.

Today’s student is much more comfortable asking “Why?”. This seems appropriate for the type of world we live in today. Any fact our students want to know can be easily accessed in a fraction of the time it took us. Therefore, it is my opinion that what we really need to teach our students is how to access the information, how to evaluate the information they find for validity, and how to use the information for a larger purpose. By ignoring corollaries, axioms, or parts of both, we are handcuffing our students and forcing them to learn the way we did without acknowledging the changing world around us.

2b. I do not have any extra corollaries or axioms to add at this time.

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